very simply put. $$(fg)^{(n)} = \sum_{k=0}^n {n\choose k}f^{(n-k)}g^{(k)},$$ where ${n\choose k} = \dfrac{n!}{k!(n-k)!}$ is the binomial coefficient and $f^{(j)}$ denotes the $j$th derivative of $f$ (and in particular $f^{(0)}=f$). Solve for n (integers only of course, not going to to play myself...
I have the given problem : A string is at rest and at time t=0 it is exposed to a constant force-distribution perpendicular from the longitude of the string. This force distribution remains for all $t>0$. Determine the signal of the string $u=u(x,t)$ if it is fastened ($u=0$ at the ends) and has ...
Going for example with the notation used in (Renner 2006), min- and max-entropies of a source $X$ with probability distribution $P_X$ are defined as $$H_{\rm max}(X) \equiv \log|\{x : \,\, P_X(x)>0\}| = \log|\operatorname{supp}(P_X)|, \\ H_{\rm min}(X) \equiv \min_x \left(-\log\left(\frac{1}{P_X(...
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